One of the largest university fraternities in the US was under a new police investigation on Tuesday after the suspension of a Florida chapter whose students set up a Facebook page allegedly advertising drugs and featuring photographs of topless or semi-nude underage girls.

Officials at Florida International University confirmed that its police department was looking into the activities of the Miami campus chapter of the Pi Kappa Alpha fraternity, which is already facing a lawsuit in Illinois over the hazing death of student David Bogenberger in November.

The Facebook page has since been taken down, but screen grabs leaked to the Miami Herald and Miami New Times last week show posts from students seeking cocaine or selling Adderall, a popular stimulant “study drug” that enables users to stay awake.

In addition, a caption below one photograph of a topless girl claims she was 17 when the picture was taken.

National leaders of the fraternity have suspended the Florida chapter for the “disgraceful, offensive and indefensible” behaviour of some of its members and, in a statement by executive vice-president Justin Buck, promised to support the police and university investigations to “hold individuals accountable to the fullest extent of the law”.

But the episode in which students allegedly posted cellphone numbers advertising the services of a campus “Pike Pharmacy”, referring to the fraternity’s nickname, and added other obscenity-laden messages and photographs, is more unwelcome publicity at a delicate time for Pi Kappa Alpha’s leadership.

The worst incident, the death of freshman student Bogenberger, 19, from alcohol poisoning after a drinking game that was part of an initiation ritual at Northern Illinois University last November, led to a wrongful death lawsuit from the teenager’s family. They claim he and others passed out after being made to drink excessive quantities of vodka in separate rooms and that organisers of the unsanctioned party discussed calling for medical help but decided against.

But the fraternity, which boasts more than 250,000 past and present members, and whose mission statement is to “develop men of integrity, intellect, and high moral character”, is no stranger to other controversies, many of them alcohol-related.

In Florida, its chapters have been suspended from several campuses in recent years, including the University of Miami, Florida Atlantic University and the University of Central Florida.

“It’s a hard nut to crack,” Dr Walter Kimbrough, an expert on the role of university fraternities and president of Dillard University, New Orleans, told the Guardian on Tuesday.

“Every year they have intense education and training programmes, they work really hard to change that behaviour, but these incidents just keep coming. They must feel kind of helpless.

“There are parents sending their kids off to college, seeing all this going on and thinking that as a national fraternity you guys aren’t doing something right. For the leadership it’s continually dampening down fires, and with these very high-profile cases they have two wildfires burning right now.”

Mark Rosenberg, the FIU president, announced that the chapter would be suspended indefinitely and called the episode “a learning opportunity”.

“The Facebook posts disgusted me, angered me and saddened me,” he said in a message addressed to the “leaders of Greek organisations” on campus. “Pi Kappa Alpha will no longer be part of our university.

“College years are a transformative period when young adults make the transition to adulthood and, we hope, learn to become respectful law-abiding citizens and leaders in our community.”

Justin True, director of communications at the Memphis, Tennessee, headquarters of the Pi Kappa Alpha fraternity, declined a request from the Guardian for an interview. “We are not open for any additional questioning regarding the former FIU chapter,” he wrote in an email, suggesting that the fraternity had expelled the group. The chapter was the subject of eight disciplinary actions in five years, according to FIU records.

Dr Kimbrough said the episode highlights the need for students to think of the consequences before using popular sites such as Facebook and Twitter. “Social media hasn’t been their friend. If anything it makes it easier for them to be caught,” he said. “This isn’t the first time. Every year someone gets suspended because somebody posts something on social media.”